I am looking for a description of the Plancherel Measure of $\textrm{SL}_3(\mathbb{Q}_p)$. Has this been calculated yet? I've search many places for it, but I've only found results on real/complex special linear groups and on $p$-adic general linear groups. Any help would be appreciated.

What do you need it for? Are you interested in it for its own sake? Do you know the Plancherel measure for $SL(2)$ or $GL(2)$? A wild guess is that beautiful formulas are only available for Hecke algebras associated to distinguished strata and that in principle there is an algorithm because the characters and representations of SL(N) have been classified.
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Marc PalmNov 6 '12 at 13:05

What is a $SL_3(\mathbb{Z})$-automorphic Hecke eigenfunction? You do not mean a $SL_3(\mathbb{Z}_p)$-biinvariant function, because then everything is fairly easy and I can give the answer.
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Marc PalmNov 6 '12 at 15:35

1 Answer
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This is not a complete answer but only some hints that could help you.

Bushnell, Kutzko and Henniart have shown, for a general reductive group, that the restriction of the Plancherel measure to each block of the Bernstein decomposition may be computed via isomorphisms of Hecke algebras :